class25.1.cutting forces

8/2/2019 Class25.1.Cutting Forces

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Forces and Mechanics of Cutting

Why should we know?

Power requirement for the machine tool can be

calculated

Design of stiffness, etc. for the machine

tolerances

Whether workpiece can withstand the cuttingforce


2/22


3/22

Ernst and Merchant (1941) did the first

scientific analysis

Normal = N

Along the tool = F

FC and FT along and normal to cutting along

the direction of tool movement with

velocity, v.

=N

F

sincos NSC FFF +=

sincos SNT FFF =

(1)

(2)


4/22

( )

( )

( )

=

=

+

=

+=

=

=

+=

sin

cos

cos

cossin

sincos

sincos

cossin

RF

RF

FR

FFF

FFF

FFN

FFF

T

C

S

TCN

TCS

TC

TC(3)

(4)

(5)

(6)

(7)

(8)

(9)


5/22

We can measure FC and FT using force

dynamometer. FS, FN, F, and N can be found.

FS and FN from equations 5 & 6.

F and N from 3 & 4

tan==

N

F( friction angle)=

sincos

cossin

TC

TC

FFFF

+

= Eq. 10


6/22

Cutting Force FC depends on

FC increases as t0 increasesFC decreases as rake angle increases and as

speed increases

Why FC is affected by speed:As speed goes up, shear angle goes up, and

friction reduces.

Forces can also be affected by the noseradius. Large nose radius increases force.

(Blunt tool)


7/22

Large nose radius can create positive rakeangle and cause rubbing and create plastic

deformation.


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10/22

Coefficient of friction in metal cutting range

from 0.5 to 2.0

Shows how high friction can rise on the

chip-tool interface

Forces on the tool tip are very high because

of small contact area.


11/22

Stresses

Average shear stress

Average normal stress

The area where the stress acts (area of shear plane)

AS can be increased by increasing t0. is independent of rake angle

decreases with increase in rake angle.

S

S

A

F=

S

N

A

F=

sin0

wtAS =


12/22

Consequently, normal stress in the shear

plane has no effect on the magnitude of

shear stress. Problems in finding stresses on the rake

face:

Hard to find the contact on the rake face.Stresses in practice is not uniformly distributed

on the rake face.


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Shear-angle relationship

Lets take friction angle as

Assume is independent of .Differentiate with respect to and equate to 0 (zero).

( )

( )

( ) ( )

0

0

sincossec

sin

cos

cos

t

F

A

F

wtA

RF

RF

C

S

S

S

S

C

+==

=

+=

=

In the previous slides we

called this

)(


15/22

The equation (A) shows that

If decreases and/or increases then decreases.

In practice this analysis is corrupted because ofseveral reasons like:

Shear stress is effected by normal stresses.

is effected by etc.

(see graph 8.19)

( ) ( )

22

45

90tancottan

+=

==+

o (A)


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17/22

Specific Energy

Total power = FC

V

If width of unit = W

Total energy/unit volume of material

removal.

Frictional specific energy:00t

F

Vt

VFu CCt

==

( )

000

cossin

t

FFr

t

Fr

Vt

FVu

tCCf

+

===


18/22

Power required to shear along the plane

As uf increases, shear angle decreases, andhence us goes up directly.

Thus friction plays an important part in

metal cutting.

sft

SSs

uuu

Vt

VFu

+=

=

0

( ) ( )

=

cos

sin

cos

sin

t

f

u

u


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20/22

P bl


21/22

Problem t0=0.005 in, V=400 ft/min, =10

o, =0.25, tc=0.009,

Fc=125 lb, Ft=50 lb.

What % of total energy is consumed in friction?


22/22

Summary Velocity triangle

Merchants circle

Compute Forces and obtain Fs, Fn etc based on

measuring Fc and Ft (Equations 1 to 10 of this slideset)

Calculate Shear stress and normal Stress

Specific energy

Shear angle relationships

Relationships between rake angle, velocity, shearangle and cutting force

Effect on Ft due to ve and +ve rake angle

class25.1.cutting forces

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